This document discusses correlations between various geotechnical properties and the void ratio of soils. It defines void ratio as the ratio of volume of voids to volume of solids. Typical void ratio ranges are provided for different soil types. Relationships are presented between void ratio and properties such as unit weight, moisture content, maximum and minimum void ratios, relative density, shear modulus, hydraulic conductivity, preconsolidation pressure, and compression index. Graphs illustrate how properties such as shear strength and hydraulic conductivity vary with changes in void ratio.

1. CORRELATIONS OF VOID RATIO
Presented By: Muhammad Ali Rehman

2.  Soil
 Void Ratio
INTRODUCTION

3. Soil
 To a Geotechnical Engineer,
Soil is considered to be a
three-phase material
composed of, solid (mineral
particle), water & air.

4. Void Ratio
 Total volume of a soil sample can
be expressed as:
V = Vs + Vv
V = Vs + Vw + Va
 The ratio of volume of voids to the volume of solids
is known as void ratio.
e = Vv/Vs

5. Void Ratio
 Value of void ratio depends on:
 the volumetric changes of the soil.
 the consistency
 packing of soil.
 Void ratio characterizes the compactness of the soil.
 Void ratio of loose soil is higher than that of dense soil.
 Can be determined only from undisturbed samples.
 Typical Void ratio value for
 Dense gravel: 0.3
 Loose sand: 0.6
 Clays: 0.5 < to <1.0.

6. Correlations

7. Porosity
 Void ratio is usually used in parallel with soil
porosity.
 Porosity is the ratio of volume of voids to the total
volume.
e =
𝑛
1−𝑛
Or
n =
𝑒
1+𝑒

8. Unit Weight
 The relation of Dry Unit Weight with void ratio:
𝛾 𝑑 =
𝐺 𝑠 𝛾 𝑤
1+𝑒
e =
𝐺 𝑠 𝛾 𝑤
𝛾 𝑑
− 1

9. Moisture content, Dry Density
 S.e = 𝐺𝑠. 𝑤 𝑛
 𝑤 𝑛 =
𝑆.𝑒
𝐺 𝑠
 e = 𝐺𝑠. 𝑤 𝑛 (if S=1)
 𝜌 𝑑 =
𝐺 𝑠.𝜌 𝑤
1+𝑒
(𝜌 𝑤 = 1000 kg/𝑚3
)

10. emax & emin
 The maximum and minimum void ratios for granular soils
depend on several factors, such as:
 Grain size
 Grain shape
 Fine contents, Fc (that is, fraction smaller than 0.075 mm)
 emax is the void ratio of soil in loosest state
 emin is the void ratio of soil in densest state

11. emax & emin
 The amount of non-
plastic fines present in
a given granular soil
has a great influence
on emax and emin.
Influence of fines on void ratio
of Nevada Sand, Lade et al.
(1998)

12. emax & emin
 Miura et al. (1997) determined the maximum and
minimum void ratios of a larger number of clean
sand samples.
emax ≈ 1.62emin

13. emax & emin
 Cubrinovski and Ishihara (2002) and Patra et al.
(2010).

14. emax & emin
 Cubrinovski & Ishihara (2002) studied the variation
of emax and emin for very large number of soils.
 Clean Sand (Fc = 0 to 5%)
emax = 0.072 + 1.53emin
 Sands with fines (5 < Fc ≤ 15%)
emax = 0.25 + 1.37emin
 Sands with fines (15 < Fc ≤ 30%)
emax = 0.44 + 1.21emin
 Silty soils (30 < Fc ≤ 70%)
emax = 0.44 + 1.32emin

15. emax & emin With Mean Grain Size
 Plot of emax - emin versus the mean grain size (D50):
Cubrinovski and Ishihara (2002)

16. Relative Density
 Relative density is commonly used to indicate the in
situ denseness or looseness of granular soil.
Dr =
𝑒 𝑚𝑎𝑥 − 𝑒
𝑒 𝑚𝑎𝑥 −𝑒 𝑚𝑖𝑛
Dr = relative density (usually in percentage)
e = in situ void ratio
emax = void ratio of soil in loosest state
emin = void ratio of soil in densest state

17. Shear Modulus
 The small-strain shear modulus of soils, Gmax, is an
important parameter for many geotechnical design
applications, including site characterization, settlement
analyses, seismic hazard analyses, and site response
analysis and soil-structure interaction.
 Hardin (1978) suggested that Gmax for clays depends
on the in situ (or applied) stress (σ'), void ratio (e), and
OCR.
 The effects of OCR are, to a large extent, taken into
account by the effect of void ratio and could be
neglected, (Leroueil and Hight, 2003).

18. Shear Modulus
Hardin (1978) and
Hight & Leroueil (2003):
Void Ratio, e

19. Hydraulic Conductivity
 One of the most important and useful parameter in the study of
percolation process in porous media, consolidation & settlement of
soils and foundation, water regime in stratified deposits, and other
geotechnical problem.
 Kozney-Carman relation, (Kozney 1927 and Carman 1937):
k: hydraulic conductivity (m/s)
e: void ratio,
Ss: specific surface area (𝑚2
/𝑔)
CF: shape factor { ≈ 0.2 (Taylor, 1948)}
γw = unit weight of water (N/𝑚3
)
ρm = density of soil (kg/𝑚3
)
μ = Viscosity of fluid (N.s/𝑚2
)

20. Hydraulic Conductivity
 Carrier (2003) has modified the Kozney-Carman
relation into:
k = 𝟏. 𝟗𝟗 × 𝟏𝟎 𝟒 𝟏
𝑺 𝑺
𝟐
×
𝒆 𝟑
𝟏+𝒆
Carrier (2003) further suggested that:

21. Hydraulic Conductivity
 Taylor (1948) and Lambe & Whitman (1969)
proposed:
Ck: permeability change index i.e. the
slope of e versus log(k) plot
k0: hydraulic conductivity for
reference void ration e0

22. Hydraulic Conductivity
 Samarasinghe et al. (1982) proposed an equation:
C: constant with same unit as k,
n: constant that depends on type
of soil and varies from 3.2 to 14.2

23. Hydraulic Conductivity
 Variation in hydraulic conductivity with void ratio:
Mesri & Olson (1971)

24. Void Ratio-Pressure Plot
 Typical plot of void ratio against effective pressure
(semi logarithmic scale)
e0: initial void ratio of specimen
e1: void ratio after consolidation caused
by pressure increment σ’1
e2: void ratio at the end of consolidation
caused by next increment of
pressure σ’2

25. Pre-consolidation Pressure
 Cassagrande (1936) proposed a simple graphical
method to determine the pre-consolidation pressure
from laboratory e-logσ’ plot.
 Draw a horizontal line ab.
 Draw the line ac tangent at a.
 Draw the line ad, which is the
bisector of the angle bac.
 Project the straight-line portion
gh of the e-log σ’ plot back to
intersect line ad at f.
 The abscissa of point f is the
pre-consolidation pressure (σ’c).

26. Pre-consolidation Pressure
 Nagaraj & Murty (1985):
e0: in situ void ratio
eL: void ratio at liquid limit =
𝐿𝐿 (%)
100
. 𝐺𝑠
Gs: specific gravity of soil
σ’0: in situ effective overburden pressure (kN/𝑚2)

27. Cc : Compression Index
 Rendon-Herrero (1983) gave the relationship for the
compression index in the form:
𝐶𝑐 = 0.141𝐺𝑠
2 1+𝑒0
𝐺𝑠
2.38
𝐶𝑐 = 1.15(𝑒0- 0.27) by Nishida (1956) – all clays
𝐶𝑐 = 0.156𝑒0 + 0.0107) by Hough (1957) – All clays
𝐶𝑐 = 0.30(𝑒0- 0.27) by Hough (1957) – inorganic cohesive soils
𝐶𝑐 = 0.30(𝑒0- 0.27) by Hough (1957) – low plasticity soils
𝐶𝑐 = 0.208𝑒0 + 0.0083 by Hough (1957) – Chicago Clays

28. Variation of Void Ratio with Shearing
Displacement
At large shear displacement, the void ratios of loose
and dense sands become practically the same, and
this is termed the critical void ratio.

29. Variation of tan𝜙’ with Void Ratio
 Acar, Durgunoglu, and Tumay (1982)
Figure shows the results of direct shear tests
conducted with a quartz sand and concrete,
wood, and steel as foundation
materials, with σ’ =100 (kN/𝑚2
).

30. References
 Principles of Geotechnical Engineering, 7th Ed, B.M. Das
 An Introduction to Geotechnical Engineering, Robert D. Holtz, and
William D. Kovacs
 Soil Mechanics in Engineering Practice, 3rd Ed, Karl V. Terzaghi,
Ralph B. Peck, and Gholamreza Mesri
 Correlations between Shear Wave Velocity and Geotechnical
Parameters in Norwegian Clays, J. S. L’Heureux and M. Long

 S. M. Rezwan Hossain, MD. Abdul Qaiyum Talukder, Shariful Islam,
MD. Rafiue Islam, “Significance of Silt Content and Void Ratio on the
Hydraulic Conductivity of Sand-Silt Mixtures”, International Journal
of Advanced Structures and Geotechnical Engineering ISSN 2319-
5347, Vol. 02, No. 04, October 2013